Say you have two hoses, A and B, that fill up a pool of equal size at different rates.
Hose A fills up a pool in 10 mins, hose B in 20 mins. Thus A = 1p/10m, B = 1p/20m.
Lets say that Hose A filling ...

Okay, so I think I kind of get this one already. Since 2 is the lowest rational number in the set that's less than $x$, then $\inf S = 2$.
But is there is any other way to explain this? I feel like ...

Here is a problem I face practicing the theory of rings:
Define $\phi : \mathbb{Z}[t] \to \mathbb{Q}$, a ring homomorphism (it does map $1$ to $1$). I'm trying to show that if $\phi(t)=\frac{u}{v}$ ...

By definition, a set $S$ is called countable if there exists an bijective function $f$ from $S$ to the natural numbers $N$.
If we take a function $g\colon\mathbb{Z\times N\to Q}$ given by $g(m, n) = ...

Does there exist any positive integer $n$ such that $e^n$ is an integer ? I was in particular trying to prove $\log 2$ is irrational ; now if it is rational , then there are relatively prime integers ...

I have a set of rational numbers, and the only allowed operation is calculating the mean of a subset and adding it to the set. The goal is to generate zero.
I tried brute-forcing this problem with S ...

Forgive me for asking such a broad question, but I really do have very little knowledge on how to do this and it came up in a problem that I have been working on for some time now, so any help would ...

I'm studying Dedekind's Cuts and his construction of Real numbers from the Rational ones. Here we are allowed to use $\Bbb{Q}$ as an ordered field and all all its properties (Archimedean Property, his ...

For example: $$\lim_{n\to\infty}\sum_{i=1}^n\frac{n-1}n\frac{1+i(n-1)}n $$
And would the result necessarily be rational, because each term appears to be the multiplication of two rational fractions?
...

$13/92=0.14\overline{1304347826086956521739}$
In this example, the length of nonrepeating part is $3$. The length of repeating part (repeating period) is $21$.
I collected some properties related to ...

Given a rational number $a/b$ expressed in simplest terms (so $GCD(a,b)=1$), I want to raise it to an integer power $n$.
I think the result will always automatically be in simplest terms, but it's a ...

I need to prove that $\log_{10}{2}$ is irrational. I understand the way this proof was done using contradiction to show that the even LHS does not equal the odd RHS, but I did it a different way and ...

Is the set of rationals a subset of the irrationals? I always assumed it was, but given that irrationals are defined to be numbers that have an infinite, non-repeating decimal expansion, there cannot ...